The movie plays in a very small resolution
That shouldn't happen. The movie should be playing in full screen, no matter the resolution your desktop uses.
The game runs in a fixed resolution (1024x768), so, if, for some reason, your screen doesn't support this, this might be the reason. However, I doubt this is the case.
The black screen after the intro is normal (at least, I remember it always being there). However, it should only last a few seconds.
I would suggest to take a look if you have the latest version of DirectX 9. If you use Vista, Win 7 or Win 8, you may not have DX 9 at all, because they don't come with it pre-installed. You can get the latest version here
Also, try to set an exception for GalCiv in your AV software. It may be a long shot, but I recently heard of several people having problems with their games due to the AV they are running (especially NWN2 in combination with AVG).
I hope that, between this, and what Support tells you, you find a solution for your problem.